Question: Kevin is 40 years younger than Gabriela. Gabriela and Kevin first met 3 years ago. Five years ago, Gabriela was 5 times as old as Kevin. How old is Gabriela now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Kevin. Let Gabriela's current age be $g$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $g = k + 40$ Five years ago, Gabriela was $g - 5$ years old, and Kevin was $k - 5$ years old. The information in the second sentence can be expressed in the following equation: $g - 5 = 5(k - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = g - 40$ . Substituting this into our second equation, we get the equation: $g - 5 = 5($ $(g - 40)$ $ -$ $ 5)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 5 = 5g - 225$ Solving for $g$ , we get: $4 g = 220$ $g = 55$.